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# Among the first ten cyclists who crossed the finish-line, 4

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Manager
Joined: 22 May 2007
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Among the first ten cyclists who crossed the finish-line, 4  [#permalink]

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26 Jul 2008, 20:53
Among the first ten cyclists who crossed the finish-line, 4 were Italians and 8 represented Telefonica team. How many cyclists who represented Telefonica team and finished in the top ten were not Italians?

1. 2 Italians who finished in the top ten did not represent Telefonica team
2. Each of the top ten finishers either was an Italian or represented Telefonica team or both

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Senior Manager
Joined: 06 Apr 2008
Posts: 390

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26 Jul 2008, 22:43
aaron22197 wrote:
Among the first ten cyclists who crossed the finish-line, 4 were Italians and 8 represented Telefonica team. How many cyclists who represented Telefonica team and finished in the top ten were not Italians?

1. 2 Italians who finished in the top ten did not represent Telefonica team
2. Each of the top ten finishers either was an Italian or represented Telefonica team or both

Will go with D)

For 1) Number of top ten finishers who were both Italian and Telefonica = 4-2 = 2
Number of telefonica team and not italians = 8-2 =6

For 2) It U Te = 10
It N Te = 8 + 4 - 10 = 2
Te = 8-2 = 6
Senior Manager
Joined: 10 Mar 2008
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29 Jul 2008, 11:41
Guys, for solving such problems would you recommend using a double set matrix or venn diagram?
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Joined: 30 Apr 2008
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Location: Oklahoma City
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29 Jul 2008, 11:46
I think it's A.

From the stem, we don't know for sure how many italians represent Telefonica. We know the numbers given add up to 12, so at least 2 have to represent Telefonica or there would not be overlap. But, this doesn't rule out that every Italian could represent team Telefonica.

A tells us that 2 Italians that finished in the top 10 did not represent team Telefonica. That means 2 did! Sufficient.

#2 tells us the same information we can deduce from the stem. There is at a minimum an overlap of 2 riders. Let's break down what #2 tells us. Each of the top 10 was an Italian (4 of them already stated so in the stem), represented Telefonica (Stem says 8 did) or both (we already know that at least 2 over lap or we would have 4 + 6 = 10, the number in the top 10. We aren't told anything new in #2 so it's insufficient.

aaron22197 wrote:
Among the first ten cyclists who crossed the finish-line, 4 were Italians and 8 represented Telefonica team. How many cyclists who represented Telefonica team and finished in the top ten were not Italians?

1. 2 Italians who finished in the top ten did not represent Telefonica team
2. Each of the top ten finishers either was an Italian or represented Telefonica team or both

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Manager
Joined: 27 Mar 2008
Posts: 75

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29 Jul 2008, 12:06
aaron22197 wrote:
Among the first ten cyclists who crossed the finish-line, 4 were Italians and 8 represented Telefonica team. How many cyclists who represented Telefonica team and finished in the top ten were not Italians?

1. 2 Italians who finished in the top ten did not represent Telefonica team
2. Each of the top ten finishers either was an Italian or represented Telefonica team or both

A:

Given-

---------Ital------Not Ital
Tel......... ............ ..... 8
Not T...... ............ ..... 2
............ 4 .......... 6

1- (sufficient) if we can find any of the inside, we can determin sufficiency.

Ital Not Ital
Tel......... 2 .......... [6] .....8
Not T..... [2] ........ [0] .....2
............ 4 ......... 6

2- (insufficient) does not provide anything more info than what was given
VP
Joined: 17 Jun 2008
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05 Aug 2008, 17:12
aaron22197 wrote:
Among the first ten cyclists who crossed the finish-line, 4 were Italians and 8 represented Telefonica team. How many cyclists who represented Telefonica team and finished in the top ten were not Italians?

1. 2 Italians who finished in the top ten did not represent Telefonica team
2. Each of the top ten finishers either was an Italian or represented Telefonica team or both

given that : out of first 10 people,4 were italians,8 were Telefonica
we need to find rest of the two winners who are belonging to Telefonica are italians or not.
(1)this says clearly two of the four italians in top 10 are not Telefonica team members .Rest Eight telefonica members ,2 are italians and 6 are not italians SUFFI

(2)this is already known .does not add on to additional info hence is insuffi.

IMO A
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Joined: 09 Jul 2008
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05 Aug 2008, 17:30
aaron22197 wrote:
Among the first ten cyclists who crossed the finish-line, 4 were Italians and 8 represented Telefonica team. How many cyclists who represented Telefonica team and finished in the top ten were not Italians?

1. 2 Italians who finished in the top ten did not represent Telefonica team
2. Each of the top ten finishers either was an Italian or represented Telefonica team or both

If there are 10 cyclists and 12 are listed as either Italians or Telefonica representatives, can't we infer that there are 2 Italians that represent Telefonica. So, the intersection of the two sets is 2. Hence the number of Telefonica reps who were not Italians = 8- 2 = 6

What more do the choices tell us? Am I over simplifying this?

A and B just confirm this. So D
Manager
Joined: 28 Apr 2008
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24 Oct 2008, 07:35
i say D

(1) and (2) are equivalent

each one of them is sufficient- so D.

10 = 4 + 8 - X + y, where X= num of italian+telefonica, y=num of nun italian and nun telefonica

from 1- x=2 so y=0- suff

from 2 y=0 so x=2 - suff
Director
Joined: 23 May 2008
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25 Oct 2008, 01:02
another A, by way of double matrix

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Re: Overlapping &nbs [#permalink] 25 Oct 2008, 01:02
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# Among the first ten cyclists who crossed the finish-line, 4

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